# A-level Physics (Advancing Physics)/Damping/Worked Solutions

1. Draw a graph of displacement for a critically damped oscillation.

2. How would you critically damp an oscillating pendulum?

Grab the weight, move it to its equilibrium position, and stop it moving.

3. How would you damp an oscillating pendulum using only a weighted polystyrene block?

Put the block in the path of the pendulum, which will bounce off the weight, losing a bit of energy each oscillation.

4. What would the displacement graph look like for this oscillation, before and after damping began?

5. The graph above is an exponentially damped oscillation. If the displacement of the undamped oscillation is given by sin ωt, what is an approximate equation for the damped oscillation, in terms of a constant k which describes the degree to which the oscillation is damped?

$x=e^{-k\omega t}\sin {\omega t}$ If k doubles, the e-kt will be squashed to half its size along the t-axis, so as k increases, the rate of damping increases.